Marine seismic surveys usually employ seismic sensors below the water's surface, e.g., in the form of long cables or “streamers” towed behind a ship, or cables resting on the ocean floor. A typical streamer includes multiple seismic sensors positioned at spaced intervals along its length. Several streamers are often positioned in parallel over a survey region.
An underwater seismic wave source, such as an air gun, produces pressure waves that travel through the water and into the underlying earth. When such waves encounter changes in acoustic impedance (e.g., at boundaries or layers between strata), some of the wave energy is reflected. The seismic sensors in the streamer(s) detect the seismic reflections and produce output signals. The sensor output signals are recorded, and later interpreted to infer structure of, fluid content of, and/or composition of rock formations in the earth's subsurface.
Traditional data acquisition has been driven by the Shannon-Nyquist sampling theorem that, in essence, a continuous signal cannot be reconstructed from its samples unless the sampling rate is at least twice the signal's maximum frequency. (This theorem applies to both time sampling and spatial sampling.) “Compressed sensing”, also called “compressive sampling”, relaxes the strictures of the Shannon-Nyquist theorem, either by recognizing and exploiting structure in the sampled signals that reduces their information content, or by allowing some information loss to occur during the sampling process (i.e., “lossy” sampling). In effect, the compressed sensing technique combines a sampling operation with a compression operation in a manner that enables sparse sampling, advantageously reducing the volume of acquired and recorded sample data. A subsequent operation can be employed to reconstruct traditional signal samples and/or the analog signals. Such processing can be performed offline, e.g., in an environment having more time and resources for data processing and storage.
Data acquisition using compressed sensing techniques is akin to lossy data compression, so there is a tradeoff between a total number of sensors employed and the quality of the resultant survey data. For signals with low information density, like seismic signals, this tradeoff is worthwhile. In the recent paper “Optimized Compressed Sensing for Curvelet-based Seismic Data Reconstruction” by Wen Tang, Jianwei Ma, and Felix J. Herrmann, available at http://dsp.rice.edu/sites/dsp.rice.edu/files/cs/OPCRSI3.pdf and incorporated herein by reference in its entirety, the authors propose an under-sampling scheme that favors sparsity-promoting recovery. The Tang paper teaches, among other things, that seismic survey data can be acquired using substantially fewer sensors, albeit sensors carefully placed at predetermined locations. The locations can be determined in a number of ways, ranging from a random scattering to a closed-form solution derived from the expected spatial frequency content of the signals. The Tang paper provides a good compromise between expediency and performance using an “optimized” random solution.
Conventional marine seismic streamers can often be 12 kilometers (km) long, and may include hundreds, or even thousands of seismic sensors. The sheer scale of this array creates reliability concerns which are typically addressed by building the streamers out of similar, interchangeable streamer sections. If there is a problem with one of the streamer sections, the problematic streamer section is replaced by a similar streamer section. In addition, streamer sections are much easier to handle and store than whole streamers. The prior art fails to suggest a streamer for compressed sampling that can adequately address such reliability concerns.